Problem: Simplify the following expression: $x = \dfrac{84k - 72}{-84k - 36}$ You can assume $k \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $84k - 72 = (2\cdot2\cdot3\cdot7 \cdot k) - (2\cdot2\cdot2\cdot3\cdot3)$ The denominator can be factored: $-84k - 36 = - (2\cdot2\cdot3\cdot7 \cdot k) - (2\cdot2\cdot3\cdot3)$ The greatest common factor of all the terms is $12$ Factoring out $12$ gives us: $x = \dfrac{(12)(7k - 6)}{(12)(-7k - 3)}$ Dividing both the numerator and denominator by $12$ gives: $x = \dfrac{7k - 6}{-7k - 3}$